First, be aware that thereFirst, be aware that there are some flowering plum trees which are ornamental and do not produce fruit. If it's a fruit-bearing tree, plum trees do not start bearing fruit until they are five or six years old. There are a number of reasons for trees of fruit-bearing age to have issues. The main reasons are: frost damage, lack of pollination, extreme temperatures, or other weather conditions (too rainy or windy).